The derivative of f (x, y, z) = x/y² + z² at the point Po(-2,-1,-1) in the direction of ü= (1,2,–2)is : %3D O None of these O v2 O v2/3 1/3

Q: [Q1] (a) The force P= -40 i + 80 j N located at r= 3 i m is the resultant of a couple C1 = -150 k…

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Q: 1. Show that the following vector field is conservative: F = (4 xy - 2z)î +(2 xr² - 6 yz ) j +(-3 y²…

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Q: For the vectors A = 8.0m South and B = 15.0 m, 30° E of N, use the method of components to find the…

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Q: - Find the area enclosed by the curve a'x = y'(2a-y)

A: “Since you have asked multiple question, we will solve the first question for you. If youwant any…

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A: Given f(x,y) =5y3x2 ;(-2,-1)

Q: 1- The work done by the force F 41-31+2 k to displace a body from point (3,2,-1) to point (2,-1,4)…

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Q: 1. Show that the following vector field is conservative: F (4 xy - 2z)î +(2 x² - 6 yz ) ĵ +(-3 y² -…

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Q: (B) Construct the analytic function ƒ(z) = u(x, y) + iv(x, y) of which the real part is: u(x, y) =…

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Q: 5. The temperature at the point (z,y) on a metal plate is modeled by T(x,y) 400e-(+)/2 in °C, with…

A: Given: T(x,y) = 400e-(x2+y)/2 Point = (3,5) To find: Direction in which there is no change in T

Q: Consider a vector field v(x, y, z) defined by v = (sin y - cos z)i + (2x + cos z) cos(y)j + (x − sin…

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Q: Find solutions for the divergence and curl of the vector field y at (1, 0, -1). v (x, y, z) = x²z²į…

A: The vector field is V=x2z2i⇀+xyzj⇀+zcosy4k⇀. The position is (1,0,-1) The divergence is ∇·V is the…

Q: R1 100 R2 ww R3 2002 D R4 www 1002 1092 R5 R6 100

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Q: If |A +B| = |A – B| then, the angle between A and B is: (a) 0° (c) 60° (b) 90° (d) 180°

A: Let us consider, A = Magnitude of A → B = Magnitude of B → θ = Angle between two vectors   It is…

Q: P 2R R The center of the charged circle of radius R = 50cm in the x-z plane is coincident with the…

A: Option e is correct 10^13 /135 (N/C)

Q: H.w: For A = 2i + 3j and B=-li+5j, find the component of A along Band the projection of A onto B.

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Q: The Eckert projection is a conformal projection.  True False

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Q: the quantity that have magnitude with no direction is scalar vector

A: Scalar quantity - A quantity has only magnitude but no direction are called a scalar quantity…

Q: X NOOZ OON yº 45 AV NO

A: To Find :  The resultant and direction of the force . Free Body Diagram : The F.B.D is,

Q: Q6- The intervertebral disc as shown below is subjected to four parallel loadings (F,, F2, F3, F4).…

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Q: magnitude of the momenr done by the force about the "z-axis" in the following figure

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Q: Determine the X and Y components of 4 N as shown in figure +y ¢ Fy 30° +x Fx

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Q: A (-3,7) y, m F=6kN x, m B (10,-8)

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A: Given : u = i+j-k v = 2i+j+k

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Q: O O O O If f(x.y, z) = xy + yz + xz. The maximum rate of change off at the point P(1,2,3) is: %3D 50…

A: Given that :  F( x ,y, z) = xy + yz + zx and the given point is  p = (1 , 2 ,3)

Q: 6. What is the vector cross product ŕ × v? r = −3i+3j4k and = -4i- 4j + 3k

A: Absolutely! Here's how to find the vector cross product r x v:1. Set up the Determinant:The cross…

Q: H.W: find the tangent plane and normal line of the surface f(x, y, z) = x + 2xy- y? + z2 = 7 at the…

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Q: 1.5 m/C B 1.5 m P= 0.8 kN T-1.2 kN 3 m 2 m 1.5 m 1 m, 3m D - Determine the x-, y-, and z- components…

A: Given: The tension along the cable CD, T = 1.2 kN The tension along the cable GF, P = 0.8 kN

Q: A wire of charge Q1 is bended into the shape of a semicircular wire of radius R, and located in a…

A: Q2 at  0,R4.3.